This should be fairly straightforward. (And yours is a
unique situation which will dictate my following opinions.)
Moved to the UK November 29, 2018
He surrendered his green card in January, but held it through the end of 2018
I did not work for the remainder of 2018 after arriving in the UK, but my husband began work for the UK entity immediately
We previously filed married filing jointly in the US
Where do I start/how do I file?
IMO, file as married joint for 2018,
somewhat similar** to your past filings. (**exception to follow)
Going forward, since your husband abandoned his green card, you will have a decision to make for 2019 filing, but, for you, it would likely be married separate for 2019.
I understand we probably need an extension - do I need to pay the tax penalty from my 403b withdrawal before then?
Why? First, you have until 15 June to file since you will not be in the US on 15 April (or is it the 17th this year?).
BUT, any tax due (estimated payment) must be paid before 15 April to avoid a penalty, even if filing an extension.
What does the extension mean towards proving UK domicile?
Your husband already likely has UK domicile (if UKC).
You do not, and an extension for 2018 will have no bearing on 'domicile'. As for your UK 'residence' (if for FEIE, 2555 - physical presence/bona fide res.), which is something entirely different from domicile, by the time you file 2019 you should qualify if you remain abroad.
You did not have any foreign income during December, and have no need to claim FEIE for 2018.
Do I need to file an FBAR? (I opened a bank account in December, but it has not had more than $10k in it)
FBAR is an aggregate total of the maximum amount,
at any time, in
all foreign accounts over which you have signature authority during the tax year. Just your one account, or did you and your husband have an additional joint account(s)? There are other considerations besides 'bank' accounts.
We had health insurance coverage through the end of November, then the NHS in December
Check the IRS publications, but I believe there is a grace period of at least 1 month (perhaps 3?) a year during which you may not have insurance, and there is no penalty. Check to be sure.
I made a withdrawal of my 403b before leaving the US, which does carry a tax penalty that I need to pay and have not yet
Make a pre- 2018 return estimated payment before 15 April to avoid the penalty, as mentioned above.
How do we present my husband's UK income for that last month toward US taxes?
** the exception for 2018!In your jointly filed return, include a form 1116, Foreign Tax Credit, which will based on the amount of tax withheld from your husband's UK pay for December 2018.
File as normal but include Form 1116, Schedule 6 to note your foreign (change of) address, Schedule 3 for transitioning 1116 to 1040, and be sure you file Schedule B and complete Part III.
Moving forward:
We moved from New York City. Anyone have any experience coming from there and proving UK domicile so as not to continue paying state/local taxes?
Others can comment on this, but I believe New York is a 'sticky' State, so you may need to terminate everything to do with NY from financial accounts to library cards.
In 2019 (and beyond) will I still need to file with my husband? (He surrendered his green card, but we did file married/jointly for years before)
Does your husband still want to be filing US tax returns on his UK income? There is a way, but most would avoid it with the USC filing MFS. It gives your husband a great deal of options for investment (and other freedoms) that he wouldn't have if filing MFJ with you.
Also, I never paid for tax help in the US, and would prefer not to start now. However, I am not unwilling to explore that option, so if anyone has any place they could privately recommend to me, i'm all ears.
If you've filed your own returns in the past, nothing for 2018 should be much different, with the exception of form 1116 FTC.
Good luck, although some may disagree with my comments (MFJ for 2018). Hopefully they will also respond.